[-] Show simple item record

dc.contributor.advisorBanks, Wiliameng
dc.contributor.authorGuo, Victor Zhenyueng
dc.date.issued2017eng
dc.date.submitted2017 Springeng
dc.description.abstract[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This thesis is focus on the methods of exponential sums and sieve methods applying to distribution of primes numbers in several forms, such as Piatetski-Shapiro primes, Beatty sequences, almost primes and primes in arithmetic progression. In the end, we also think about the classical problem in Burgess bound. We begin by explaining the importance of the methods of exponential sums. Together with sieve methods, we investigate the Piatetski-Shapiro primes from almost primes and the intersection between Piatetski-Shapiro primes and Betty sequences. Above all, we study primes in several forms from a "thin" integer set. We also study the distribution of consecutive prime numbers from two Beatty sequences by an assumption of a well-known conjecture. Finally, we turn to the methods of character sums and the problem of the least quadratic nonresidue. We improve the best known bound by changing the arbitrary small constant into a reciprocal of an infinite function. Possible future work is also discussed in the thesis.eng
dc.identifier.urihttps://hdl.handle.net/10355/61884
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rightsAccess to files is limited to the University of Missouri--Columbia.eng
dc.subject.FASTNumbers, Prime -- Study and teachingeng
dc.subject.FASTSequences (Mathematics)eng
dc.titleExponential sums, character sums, sieve methods and distribution of prime numberseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


Files in this item

[PDF]
[PDF]
[PDF]

This item appears in the following Collection(s)

[-] Show simple item record